The top drawer folks in France had no interest in arming former Burgundians, or Bretons, or Gascons, or Italians, or Swiss, or..... GERMANS! Eventually they had to, but the English nailed them when they were weak ~
That's a very good point. Britain faced a very similar situation, in that the Brits were trying to incorporate into one army Irish, Welsh, Scots, Saxons, Normans and people from Brittany, Gascony and other portions of what ultimately became France, but which had been under English control since Eleanor of Aquitaine and Henry II had been married. The author of the book I mentioned earlier stated that Edward III, or maybe it was Henry V, had a greater claim to the French throne by birth than did the French claimant at that time. Ultimately, the diversity of Great Britain became its strength (sorry, I just had to go there) as these diverse peoples were unified in their hatred of all things French.